Explanation:
Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0.
1. 2x + 4 = 2
2x - 2 = 0
No, it's not a quadratic equation as it is not in the form of ax² + bx + c
2. 1/2x + 7x² = 2
on solving,
7x² + 1/2x = 2
14x² + x / 2 = 2
14x² + x = 4
14x² + x - 4 = 0
yes it's a quadratic equation
3. 7 + x² = 7x + x² - 5
x² - x² - 7x = - 12
- 7x = -12
no it is not a quadratic equation
4. 5x + x³ = 3
no it's not a quadratic equation as the highest degree is 3
5. (x + 4)(x - 3)
x(x - 3) + 4(x - 3)
x² - 3x + 4x - 3
x² + x - 3
yes it is a quadratic equation.
6. x(x + 5)² - x³ = 1
x(x² + 10x + 25) - x³ = 1
x³ + 10x² + 25x - x³ = 1
10x² + 25x - 1 = 0
yes it is a quadratic equation.
7. 3x² + x + 2
yes it is a quadratic equation
8. x² = - x - 22
x² + x + 22 = 0
yes it is a quadratic equation
9. (x + 1) (x - 1) = 0
(identity) ={ (a +b) (a - b) } = a² - b²
x² - 1 = 0
it's a quadratic equation
10. 23 = 7x² - x
7x² - x - 23 = 0
yes it's a quadratic equation.